International Centre for Theoretical Sciences - TIFR
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Email: [email protected] Website: www.icts.res.in
ICTS Seminar
Title : Geometry and Integrability of Mechanics on Curved Spaces Speaker : Sumanto Chanda, S.N. Bose National Centre for Basic Sciences, Kolkata
Date : Wednesday, August, 8, 2018 Time : 2:00 PM
Venue : Emmy Noether Seminar Room, ICTS Campus, Bangalore
Abstract : The topic of integrable systems deals with ideally solvable non-linear differential equations, such as those dealt with in the study of mechanics on curved spaces. Such systems are also suspected to be various reductions of Yang-Mills systems. In this seminar, I will explore formulation of Jacobi metric for a time-independent spacetime metric as an effective reduction of the geodesic to lower dimensions. A similar formulation will then be demonstrated for a spacetime metric dependent on time, involving the Eisenhart-Duval lift as a vital step, followed by the application of Jacobi metric formulation to Kepler and oscillator systems. I will then talk about the generalized DarbouxHalphen system as a reduction of self-dual Yang- Mills equation, and the formulation of its Lax-Pair and Hamiltonian, followed by its connection to the self-dual Bianchi-IX gravitational instanton. Finally, I will briefly discuss the geometric formulation of relativistic mechanics for accelerating bodies on curved spaces.
